A physical paradox
is an apparent contradiction in physical
descriptions of the universe.
While many physical paradoxes have accepted resolutions, others defy
resolution and may indicate flaws in theory.
In physics as in
all of science, contradictions
and paradoxes
are generally assumed to be artifacts of error and incompleteness
because reality
is assumed to be completely consistent,
although this is itself a philosophical assumption. When, as in
fields such as quantum
physics and relativity
theory, existing assumptions about reality have been shown to
break down, this has usually been dealt with by changing our
understanding of reality to a new one which remains self-consistent
in the presence of the new evidence.

Another paradox associated with relativity is Supplee's
paradox which seems to describe two reference
frames that are irreconcilable. In this case, the problem is
assumed to be well-posed in special relativity, but because the
effect is dependent on objects and fluids with mass, the effects of
general
relativity need to be taken into account. Taking the correct
assumptions, the resolution is actually a way of restating the
equivalence
principle.

Similarly, there exists a set of physical paradoxes that directly
rely on one or more assumptions that are incorrect. The Gibbs
paradox of statistical
mechanics yields an apparent contradiction when calculating the
entropy of
mixing. If the assumption that the particles in an ideal
gas are indistinguishable is not appropriately taken into
account, the calculated entropy is not an extensive
variable as it should be.

Olbers'
paradox shows that an infinite universe with a uniform
distribution of stars necessarily leads to a sky that is as bright as
a star. The observed dark night sky can be alternatively resolvable
by stating that one of the two assumptions is incorrect. This paradox
was sometimes used to argue that a homogeneous
and isotropicuniverse as
required by the cosmological
principle was necessarily finite in extent, but it turns out that
there are ways to relax the assumptions in other ways that admit
alternative resolutions.

Mpemba
paradox is that under certain conditions, hot water will freeze
faster than cold water even though it must pass through the same
temperature as the cold water during the freezing process. This is a
seeming violation of Newton's
law of cooling but in reality it is due to non-linear
effects that influence the freezing process. The assumption that only
the temperature
of the water will affect freezing is not correct.

Paradoxes relating to unphysical mathematical idealizations

A common paradox occurs with mathematical idealizations such as
point sources
which describe physical phenomena well at distant or global scales
but break down at the point
itself. These paradoxes are sometimes seen as relating to Zeno's
paradoxes which all deal with the physical manifestations of
mathematical properties of continuity,
infinitesimals,
and infinities
often associated with space
and time. For
example, the electric
field associated with a point
charge is infinite at the location of the point charge. A
consequence of this apparent paradox is that the electric field of a
point-charge can only be described in a limiting sense by a carefully
constructed Dirac
delta function. This mathematically inelegant but physically
useful concept allows for the efficient calculation of the associated
physical conditions while conveniently sidestepping the philosophical
issue of what actually occurs at the infinitesimally-defined point: a
question that physics is as yet unable to answer. Fortunately, a
consistent theory of quantum
electrodynamics removes the need for infinitesimal point charges
altogether.

A similar situation occurs in general
relativity with the gravitational
singularity associated with the Schwarzschild
solution that describes the geometry
of a black hole.
The curvature
of spacetime at
the singularity is infinite which is another way of stating that the
theory does not describe the physical conditions at this point. It is
hoped that the solution to this paradox will be found with a
consistent theory of quantum
gravity, something which has thus far remained elusive. A
consequence of this paradox is that the associated singularity that
occurred at the supposed starting point of the universe (see Big
Bang) is not adequately described by physics. Before a
theoretical extrapolation of a singularity can occur, quantum
mechanical effects become important in an era known as the Planck
time. Without a consistent theory, there can be no meaningful
statement about the physical conditions associated with the universe
before this point.

The "resolutions" to these paradoxes are considered by
many to be philosophically unsatisfying because they hinge on what is
specifically meant by the measurement
of an observation
or what serves as an observer in the thought experiments. In a real
physical sense, no matter what way either of those terms are defined,
the results are the same. Any given observation of a cat will yield
either one that is dead or alive; the superposition is a necessary
condition for calculating what is to be expected, but will never
itself be observed. Likewise, the EPR
paradox yields no way of transmitting information faster than the
speed of light; though there is a seemingly instantaneous
conservation of the quantum-entangled observable being measured, it
turns out that it is physically impossible to use this effect to
transmit information. Why there is an instantaneous conservation is
the subject of which is the correct interpretation
of quantum mechanics.

Speculative theories of quantum
gravity that combine general
relativity with quantum
mechanics have their own associated paradoxes that are generally
accepted to be artifacts of the lack of a consistent physical model
that unites the two formulations. One such paradox is the black
hole information paradox which points out that information
associated with a particle that falls into a black hole is not
conserved when the theoretical Hawking
radiation causes the black hole to evaporate. In 2004, Stephen
Hawking claimed to have a working resolution to this problem, but
the details have yet to be published and the speculative nature of
Hawking
radiation means that it isn't clear whether this paradox is
relevant to physical reality.

Causality
paradoxes

A set of similar paradoxes occurs within the area of physics
involving arrow
of time and causality.
One of these, the grandfather
paradox, deals with the peculiar nature of causality
in closed time-like
loops. In its most crude conception, the paradox involves a person
traveling back in time and murdering an ancestor who hadn't yet had a
chance to procreate. The speculative nature of time travel to the
past means that there is no agreed upon resolution to the paradox,
nor is it even clear that there are physically possible solutions to
the Einstein
equations that would allow for the conditions required for the
paradox to be met. Nevertheless, there are two common explanations
for possible resolutions for this paradox that take on similar flavor
for the explanations of quantum mechanical paradoxes. In the
so-called self-consistent
solution, reality
is constructed in such a way as to deterministically
prevent such paradoxes from occurring. This idea makes many free
will advocates uncomfortable, though it is very satisfying to
many philosophical
naturalists.[which?]
Alternatively, the many
worlds idealization or the concept of parallel
universes is sometimes conjectured to allow for a continual
fracturing of possible worldlines
into many different alternative realities. This would mean that any
person who traveled back in time would necessarily enter a different
parallel universe that would have a different history from the point
of the time travel forward.

Another paradox associated with the causality and the one-way
nature of time is Loschmidt's
paradox which poses the question how can microprocesses that are
time-reversible
produce a time-irreversible
increase in entropy.
A partial resolution to this paradox is rigorously provided for by
the fluctuation
theorem which relies on carefully keeping track of time averaged
quantities to show that from a statistical
mechanics point of view, entropy is far more likely to increase
than to decrease. However, if no assumptions about initial boundary
conditions are made, the fluctuation theorem should apply equally
well in reverse, predicting that a system currently in a low-entropy
state is more likely to have been at a higher-entropy state in the
past, in contradiction with what would usually be seen in a reversed
film of a nonequilibrium state going to equilibrium. Thus, the
overall asymmetry in thermodynamics
which is at the heart of Loschmidt's paradox is still not resolved by
the fluctuation theorem. Most physicists believe that the
thermodynamic arrow
of time can only be explained by appealing to low entropy
conditions shortly after the big
bang, although the explanation for the low entropy of the big
bang itself is still debated.

Observational
paradoxes

A further set of physical paradoxes are based on sets of
observations that fail to be adequately explained by current physical
models. These may simply be indications of the incompleteness of
current theories. It is recognized that unification
has not been accomplished yet which may hint at fundamental problems
with the current scientific
paradigms. Whether this is the harbinger of a scientific
revolution yet to come or whether these observations will yield
to future refinements or be found to be erroneous is yet to be
determined. A brief list of these yet inadequately explained
observations includes observations implying the existence of dark
matter, observations implying the existence of dark
energy, the
observed matter-antimatter asymmetry, the GZK
paradox, the heat
death paradox, and the Fermi
paradox.

Are
paradoxes fundamental?

In a new book, "Irrationality in Nature or in Science?",
it is claimed that essential paradoxes in quantum physics, relativity
theory and cosmology disappear, when natural phenomena are assumed to
be fundamentally time oriented and irreversible. At present
fundamental laws are described to be time-invertible, but a
fundamental time orientation of energy properties is already
recognized in a dynamic interpretation of the principle of least
action.